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Mathematics of the USSR-Izvestiya, 1979, Volume 13, Issue 3, Pages 557–588
DOI: https://doi.org/10.1070/IM1979v013n03ABEH002077 (Mi im1967) 		 
This article is cited in 43 scientific papers (total in 43 papers)

Explicit form of the law of reciprocity

S. V. Vostokov
English version PDF (1209 kB) Citations (43)
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DOI: https://doi.org/10.1070/IM1979v013n03ABEH002077
Abstract: A pairing in the multiplicative group of a local field (a finite extension of a $p$-adic number field) is defined in terms of the expansion of elements into series in a local uniformizing parameter. The main properties of this pairing are proved: bilinearity, skew-symmetry, invariance with respect to choice of local uniformizing parameter, and independence of the choice of expansion of elements into series in this uniformizing parameter. In addition, the norm property of this pairing is examined. The main result of this paper is that this pairing coincides with Hilbert's norm residue symbol. This yields an explicit formula for the latter.
Bibliography: 9 titles.
Received: 06.06.1978
Russian version:
Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya, 1978, Volume 42, Issue 6, Pages 1288–1321
Bibliographic databases:
UDC: 519.48
MSC: Primary 12B10; Secondary 12B25
Language: English
Original paper language: Russian
Citation: S. V. Vostokov, “Explicit form of the law of reciprocity”, Izv. Akad. Nauk SSSR Ser. Mat., 42:6 (1978), 1288–1321; Math. USSR-Izv., 13:3 (1979), 557–588
Citation in format AMSBIB
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\by S.~V.~Vostokov
\paper Explicit form of the law of reciprocity
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1978
\vol 42
\issue 6
\pages 1288--1321
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=522940}
\zmath{https://zbmath.org/?q=an:0467.12018|0408.12002}
\transl
\jour Math. USSR-Izv.
\yr 1979
\vol 13
\issue 3
\pages 557--588
\crossref{https://doi.org/10.1070/IM1979v013n03ABEH002077}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1979JG49100003}
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  • https://www.mathnet.ru/eng/im/v42/i6/p1288
    • This publication is cited in the following 43 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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    Abstract page:1149
    Russian version PDF:427
    English version PDF:25
    References:80
    First page:1
     
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